A195294 Smallest palindromic prime containing the n-th palindrome as central digit(s), or 0 if no such prime exists.

101, 313, 2, 3, 11411, 5, 10601, 7, 181, 191, 11, 0, 0, 0, 0, 0, 0, 0, 0, 101, 1311131, 1212121, 131, 11411, 151, 1616161, 1117111, 181, 191, 1120211, 1221221, 72227, 32323, 12421, 3425243, 1126211, 12721, 12821, 1129211, 73037, 313, 73237, 13331, 1134311, 353

Offset

1,1

Links

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..11000

G. L. Honaker, Jr. & C. K. Caldwell, Palindromic Prime Pyramids, p. 1.

G. L. Honaker, Jr. & C. K. Caldwell, Supplement to "Palindromic Prime Pyramids"

Eric Weisstein's World of Mathematics, Palindromic Number

Eric Weisstein's World of Mathematics, Palindromic Prime

Index entries for sequences related to palindromes

Example

a(5) = 11411 because A002113(5) = 4 and 4, 141, 343, 737, 939, and 10401 are all composite, but 11411 is prime.
a(12) = 0 because A002113(12) = 22 and every palindrome with 22 in the center (22, 1221, 2222, ...) has an even number of digits, so is divisible by 11.

Mathematica

lst1 = {}; lst2 = {}; r = 353; Do[d = IntegerDigits[n, 10]; If[Reverse[d] == d, AppendTo[lst1, n]], {n, r}]; Do[a = lst1[[p]]; If[EvenQ@IntegerLength[a] && ! PrimeQ[a], AppendTo[lst2, 0], If[PrimeQ[a], b = a, n = 1; While[True, b = FromDigits[Join[Flatten@IntegerDigits@PadLeft[{a}, 2, n], Reverse@IntegerDigits[n]]]; If[PrimeQ[b], Break[]]; n++]]; AppendTo[lst2, b]], {p, Count[lst1, _Integer]}]; Prepend[lst2, 101] (* Arkadiusz Wesolowski, Jan 29 2012 *)

Crossrefs

Supersequence of A002385 (palindromic primes).

Sequence in context: A033241 A140021 A139701 * A142578 A256048 A252942

Adjacent sequences: A195291 A195292 A195293 * A195295 A195296 A195297

Keyword

base,nonn

Author

Arkadiusz Wesolowski, Sep 14 2011

Status

approved